Skip to main content
SpringerLink
Log in

Bicyclic Graphs with Nullity n−5

  • Conference paper
  • First Online:
Proceedings of The Eighth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA), 2013

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 212))

  • 795 Accesses

Abstract

Let \( G \) be a simple undirected graph on n vertices, \( A(G) \) be its adjacency matrix. The nullity \( \eta (G) \) of the graph \( G \) is the multiplicity of the eigenvalue zero in its spectrum. In this paper, we characterize the bicyclic graphs with nullity \( n - 5 \).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Collatz L, Sinogowitz U (1957) Spektren endlicher Grafen. Abh. Math Univ Hamburg, 2163–2167

    Google Scholar 

  2. Hu S, Xuezhong T, Liu B (2008) On the nullity of bicyclic graphs. Linear Algebra Appl, 4291387–4291391

    Google Scholar 

  3. Sciriha I (1999) On the rank of graphs. In: Alavi Y, Lick DR, Schwenk A (eds) Combinatorics, graph theory and algorithms, vol 2. Michigan, pp 769–778

    Google Scholar 

  4. Sciriha I (1998) On the construction of nullity one. Discrete Math 181193–181211

    Google Scholar 

  5. Sciriha I (1998) On singular line graphs of trees. Congressus Numeratium, 13573–13591

    Google Scholar 

  6. Tan XZ, Liu BL (2005) On the nullity of unicyclic graphs. Linear Algebra Appl 408:212–222

    Article  MathSciNet  MATH  Google Scholar 

  7. Cvetkovic D, Doob M, Sachs H (1980) Spectra of graphs. Academic Press, New York

    MATH  Google Scholar 

  8. Gong S-C, Fan Y-Z, Yin Z-X (2009) The tree with second largest Laplacian spread. Academic Press, Hangzhou

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Science, Anhui University of Science and Technology, Huainan, 232001, China

    Tian-tian Zheng

Authors
  1. Tian-tian Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tian-tian Zheng .

Editor information

Editors and Affiliations

  1. School of Science, Anhui University of Science & Technology, Huainan, China

    Zhixiang Yin

  2. Huazhong University of Science and Technology, Wuhan, China

    Linqiang Pan

  3. Anhui University of Science & Technology, Huainan, China

    Xianwen Fang

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zheng, Tt. (2013). Bicyclic Graphs with Nullity n−5. In: Yin, Z., Pan, L., Fang, X. (eds) Proceedings of The Eighth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA), 2013. Advances in Intelligent Systems and Computing, vol 212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37502-6_69

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-37502-6_69

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37501-9

  • Online ISBN: 978-3-642-37502-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation